Question

which image shows triangle abc dilated by a scale factor of 3 centered at the point b?

Explanation:

Step1: Recall dilation properties

Dilation centered at a point. The center of dilation (point \(B\)) remains fixed.

Step2: Analyze side lengths

For a scale factor of \(3\), the distance from \(B\) to other points (e.g., \(A\) and \(C\)) in the dilated triangle should be \(3\) times the original distance.
In the first - row right - hand image:
The distance from \(B\) to \(A'\) is \(3\) times the distance from \(B\) to \(A\), and the distance from \(B\) to \(C'\) is \(3\) times the distance from \(B\) to \(C\), while \(B\) itself is unchanged.

Answer:

The first - row right - hand image.